GREEN SUPPLY CHAIN MANAGEMENT WITH LINGISTIC
PREFERENCES AND INCOMPLEE INFORMATION
Ming-Lang Tseng, Ru-Jen Lin and Anthony SF Chiu
Graduate School of Business & Management, Lung Hwa University of Science and Technology, Taiwan
Department of Industrial Engineering, De La Salle University, Manila
E-mail: tsengminglang@gmail.com
ABSTRACT
As firms move toward environmental sustainability, management must extend
managements efforts to improve environmental practices across the supply chain. The
selection of a suitable green supplier according to green supply chain management criteria
(GSCM) is essential for the sustainable development of manufacturing firms. The objective of
this study was to select an optimal alternative in the presence of incomplete information and
linguistic preferences using multiple GSCM criteria. The goal of GSCM is to reduce a firm’s
pollution and other environmental impacts. In the proposed method, the weights of GSCM
criteria and alternatives are described using linguistic preferences that can be resolved with
fuzzy set theory. Subsequently, the rank of each alternative was calculated from incomplete
information by applying a grey degree. Moreover, a case study was used to resolve the
proposed method, and the results and managerial implications of the analysis are discussed in
detail.
Keywords: grey degree, fuzzy set theory, firm’s green supply chain management
INTRODUCTION
In recent years, environmental management has evolved to include boundary-spanning
activities in the supply chain, and both upstream and downstream activities are included in
green supply chain management (GSCM) (Sarkis, 1998; Lee et al., 2009). A limited
understanding of GSCM has hindered the development of a widely accepted framework that
characterizes and categorizes a firm’s environmental activities. The European Union has
established a variety of environmental policies, including RoHS (the restricted use of
hazardous substances in electrical and electronic equipment) and WEEE (waste electronics
and electrical equipment) Directives. These directives ban manufacturers, sellers, distributors
and recyclers of electrical and electronic equipment from launching new equipment that
contains hazardous materials on the market (Tseng, 2009a; Tseng 2010a). While WEEE
directives are aimed at the life cycle of the product, RoHS is targeted at the product design
stage. Although environmental regulations and mandatory programs have been implemented,
pressure to protect the environment also comes from other external stakeholders.
Currently, a wide variety of studies on GSCM can be found in the literature (Zhu et al.,
2008; Srivastava, 2007). Srivastava (2007) defined GSCM as a combination of environmental
and supply chain management (SCM) activities, including product design, material selection,
manufacturing processes, final product delivery and end-of-life product management.
Moreover, through GSCM, firms can select from a wide variety of suppliers and leverage
resources throughout the firm to eliminate the environmental impacts of supply chain
activities. Firms typically expect their suppliers to go beyond environmental compliance and
develop efficient, green product designs. In addition, suppliers are expected to assess the life
cycle of a product. Nevertheless, the firm’s suppliers must satisfy GSCM criteria under the
constraint of incomplete information and subjective human preferences (uncertainty);
however, this phenomenon has not been thoroughly examined.
GSCM philosophy focuses on how firms utilize the supplier’s processes and technologies,
as well as the supplier’s ability to integrate environmental concerns and enhance the firm’s
competitive advantage (Vachon and Klassen, 2008). However, to study and advance the body
of knowledge related to GSCM, identification of appropriate measures is necessary. To
effectively and empirically advance the theory, greater attention must be focused on
employing multi-criteria evaluations, assessing the validity of criteria and modifying
unacceptable criteria through extensive literature reviews (Tseng et al., 2009b; Lee et al.,
2009). Hence, in this study, a number of different criteria that can be used to evaluate GSCM
practices were integrated, and a literature review on supply chain and environmental
management was performed. Firms can benefit from the development of reliable and valid
criteria, and the practitioner can apply these criteria as benchmarks to attain continuous
improvement. One objective of the present study was to assist firms in understanding the
criteria and implementation. However, the uncertainties and incomplete information are often
encountered in the implementation process. In the process of GSCM, the selection of green
supplier is always encountered, the multi-criteria decision making (MCDM) tools are always
proposed to be applied in the process (Tseng et al., 2008).
In real systems, MCDM is often based on subjective preferences or incomplete
information. Grey theory is superior for the theoretical analysis of systems with imprecise and
incomplete information within a system of evaluation (Tseng 2010b). Moreover, the
evaluation system having incomplete information is so called grey system and the triangular
fuzzy numbers in grey system represents a set of numbers with less complete information, the
system is always represented as lack of information. Hence, the grey possible degree is to
evaluate the incomplete information. The principles of the available theories and modeling
schemes for the prediction and diagnosis of an uncertain situation are summarized, and the
practical applications of theories and linguistic preferences are reviewed. People often employ
natural language to express thoughts and subjective perceptions; however, the meaning of
words in natural languages is often vague. Although the meaning of a specific word may be
well defined, when that word is used to define a set, the boundaries of the set can become
uncertain. Hence, the proposed method uses fuzzy set theory to appropriately express the
determination of human judgment in GSCM criteria. The second contribution of this study is
the development of a hybrid approach for the establishment of GSCM criteria for the selection
of an optimal alternative.
In an effort to determine the uncertainty in the proposed model, GSCM criteria were
integrated and an optimal alternative was selected. This paper contributes to GSCM literature
by developing valid and reliable criteria based on information obtained from GSCM literature
and experts in the field. Moreover, this study developed an approach based on grey theory for
the determination of linguistic preferences. In section 2 of this paper, a literature review of
GSCM practices is provided. In addition, the methodology used to develop GSCM criteria
was validated and is presented in Section 3. Section 4 presents the results of this study, and
the implications of the results are discussed in section 5. The paper is concluded in section 6
by summarizing the results, implications, limitations and potential topics of future research.
PROPOSED GSCM CRITERIA
Contributions from industry and academia, along with the results of an extensive
literature review, were used to establish 16 criteria of an optimal supplier (Li et al., 2006;
Tseng et al., 2009b). Selection of appropriate suppliers in GSCM requires battery of
evaluation criteria, which include such information as customer focus, competitive priority,
green purchasing, information technology, and top management support of a firm. Srivastava
(2007) described GSCM as combining environmental thinking and supply chain management
and defines it as including product design, material sourcing and selection, manufacturing
processes, delivery of the final product to the consumer, and end-of-life management of the
product after its useful life. A firm must have outstanding competitive priority in order to
perform well management in production, such as producing high quality products with
excellent logistics arrangement. The competitive priority is closely related to top management
support that requires strategic purchasing. As such, the present study will view GSCM a
complex, interactive process of many different resources with multidimensional,
interdependent criteria (Sarkis, 1998; 2003).
To ensure that the profitability of the supplier (C2) is an important part of the firm’s
practices, GSCM has become critical in establishing value-added content (Kathuria, 2000;
Johnston et al., 2004; Yao et al., 2007). Moreover, the reliability of delivery (C1), defined as
the ability to meet delivery schedules or promises, and the ability to react quickly to customer
orders, is critical to improving the firm’s customer service. The product conformance quality
(C5), defined as the ability of the firm to satisfy the customer needs, is critical to the firm’s
success (Chase et al., 2001). Tan et al. (1998) explored the relationship between supplier
management, customer relations and organizational performance, and used purchasing,
quality, customer relations and relationship supplier closeness (C3) to evaluate the suitability
of a supplier selection model. Sarkis (1998) categorized environmentally conscious business
practices into five major components including green design (green design (C8)), life cycle
analysis, the total quality of environmental management and compliance with environmental
standards such as ISO 14000 (C11).
Researchers have included internal green production (C12), clean production (C14) and
the quality of internal service (C7) as GSCM criteria, and the supplier’s purchasing
perspective has also been addressed.. Carr and Smeltzer (1999) documented how firms with
strategic purchasing plans foster long-term, cooperative relationships, and achieve greater
responsiveness to the needs of their suppliers. Zhu and Geng (2001) studied Chinese firms
and examined their methods of environmental development in business practices such as
green purchasing (C9). Among the supplier selection models currently in use,
environmentally preferable bidding and life cycle assessment (C10), which assesses the
impacts of green purchasing and their financial consequences through the entire product
life-cycle, are the most popular. However, supplier flexibility (C6) is a complex and
multi-dimensional capability that requires firm-wide effort to increase the firm’s
responsiveness, reduce waste and limit the firm’s environmental impact (Dreyer and
Gronhaug, 2004). Chen, et al. (2006) identified many quantitative and qualitative factors such
as quality, price and flexibility, and concluded that delivery performance must be considered
in the determination of the optimal supplier. Humphreys et al. (2003) identified environmental
criteria that influence a firm’s management support services (C13) and developed
knowledge-based environmental management system requirements (C16) to integrate the
environmental criteria and support the supplier selection process.
GSCM capabilities are ‘‘complex bundles of individual skills, assets and accumulated
knowledge exercised through production processes, that enable firms to co-ordinate activities
and make use of their resources’’ (Olavarrieta and Ellinger, 1997). Moreover, GSCM is
essential to the competitive advantage of a firm. GSCM involves the flow of finances,
logistics, and information, as well as the ability to integrate relationships and green
technology (C4), and to reduce the use of hazardous products in the production process (C15).
Figure 1 presents the hierarchical structure of the framework used to evaluate a firm’s GSCM.
The framework consists of a MCDM analysis based on fuzzy set theory and grey degree, and
can be used to select optimal suppliers (Chen and Tzeng, 2004; Zhang et al., 2005; Li et al.,
2007). Moreover, fuzzy set theory was used to eliminate the linguistic preferences of
subjective judgment (Zadeh, 1965; Tseng et al., 2008; Tseng, 2010a). The proposed
framework is based on the following criteria: (C1) reliability of delivery; (C2) profitability of
the supplier; (C3) relationship to the supplier; (C4) green technology capabilities; (C5)
conformance quality; (C6) flexibility of the supplier; (C7) service quality; (C8) green
purchasing capabilities; (C9) life cycle assessment; (C10) green design; (C11) green
certifications; (C12) internal green production plans; (C13) management support; (C14) green
production; (C15) the reduction of hazardous materials in the production process; (C16)
environmental management systems.
Firm’s GSCM
C1
C2
Alternative 1
C3
C4
2
………..
3
C15
C16
4
Figure 1. Hierarchical structure
METHOD
Researchers describe GSCM as a strategic, decision-making perspective used to improve
the performance of a firm. This study focused on GSCM criteria and their relevant
associations, as described below. The definitions of fuzzy set theory, grey theory and the
procedures of the proposed approach are also briefly discussed.
3.1 Fuzzy set theory
Fuzzy set theory (Zadeh, 1965) is a mathematical theory designed to model the fuzziness
of cognitive processes. It is essentially a generalization of set theory, where the classes lack
sharp boundaries. The membership function  A (x) of a fuzzy set operates over the range of
real numbers on the interval of [0, 1].
An expert’s uncertain judgment can be represented by a fuzzy number. A TFN is a fuzzy
number with a membership function that is defined by three real numbers (a, b, c), where a, b,
and c are real numbers and a  b  c . This membership function is illustrated in Fig. 2 and
described mathematically below.
In the proposed method, the linguistic preferences used to derive the priorities of the
alternatives and the grey numbers used to establish the selection criteria were uncertain. The
triangular fuzzy membership function employed in the proposed model is presented as
follows (Lin et al., 2007).
~
Definition 1. A TFN N was defined as a triplet (a, b, c), and the membership function
 A (x) was defined as:
0
xa

( x  a) /(b  a) a  x  b

 ( x)  
 (c  x) /(c  b) b  x  c

0
cx
(1)
 A (x)
1
a
b
c
X
Figure 2. A TFN A= (a, b, c)
Therefore, a, b, and c represent the lower, mean and upper bounds of the TFN. The
membership function represents the degree to which any element (x) in domain X belongs to
fuzzy number A.
3.2 Grey theory
Grey theory is a mathematical theory derived from the grey set and is an effective
method used to resolve uncertainties in discrete data (Deng 1989). In this study, the basic
definitions of grey systems, sets and numbers were applied(Tseng, 2008).
Definition 2. A grey system contains incomplete information and is represented by a set of
TFNs. In the proposed model, X is the universal set, and G of X is a grey set defined by
G (x) and  G (x) .
G ( x) : x  [0,1]

 G ( x) : x  [0,1]
(2)
G ( x)  G ( x), x  X , X  R, G ( x) and  G (x) are the upper and lower membership
functions of G after defuzzification, respectively. When G (x) =  G (x) , G becomes a fuzzy
set. Thus, grey theory considers fuzzy conditions and can handle fuzzy situations.
Definition 3. TFNs can be defined as a set of numbers within a grey system. For example, the
rating of criteria and alternatives in this study are described by TFNs. The numerical interval
contains uncertain information, and the TFNs are defined as  G, (G  G  ). The lower
and upper limit of G can be estimated, and G is defined as a lower limit TFNs.
 G  [G, )

 G  (, G ]
(3)
Definition 4. The lower and upper limits of G can be estimated, and G was defined as an
interval TFNs.
 G  [G, G ]
(4)
A set of TFNs is an operation based on sets of intervals rather than real numbers. In this
study, the exact range of the corresponding operation was located on the interval
 G  [G1 , G1 ] and  G  [G 2 , G2 ] . Only the proofs of addition and subtraction were
employed.

 G1  G2  [G1 G 2 , G1  G2 ]


 G1  G2  [G1 G 2 , G1  G2 ]
(5)
Definition 5. The length of TFNs  G was defined as:
L (  G ) = [G  G ]
(6)
Definition 6. For the two set of TFNs  G1  [G1 , G1 ] and  G2  [G 2 , G2 ] , the possible
degree of  G1  G2 was expressed as:
P  G1  G2

max( 0, L *  max( 0, G1  G2 ))
L*
(7)
where L*  L(G1 )  L(G2 ) . The positive relationship between  G1 and  G2 was
determined as follows:
1. If G1  G2 and G1  G2 , that  G1  G2 , then P G1  G2  = 0.5
2. If G2  G1 , that  G2  G1 , then P G1  G2  = 1
3. If G2  G1 and G1  G2 , that  G2  G1 , then P G1  G2  = 0
4. If  G1 and  G2 overlap, and P G1  G2  > 0.5, then  G2  G1 . If
P G1  G2  < 0.5, then  G2  G1 .
3.3 Proposed approach
In this study, fuzzy set theory and grey possible degree were applied to the evaluation of
GSCM criteria. The objective of the study was to evaluate the application of fuzzy grey
degree to the determination of GSCM criteria. To rank the suitability of the alternatives, grey
theory was applied. In the proposed model, A = {A1, A2, …. Am} is a discrete set of m
possible alternatives, and C = {C1, C2,….Cn}is a set of n criteria and
 w  {w1 ,w2 ,........,wn } is the vector of criteria weights. The weights and ratings of the
alternatives were numbers located on the aforementioned interval scale. The procedures used
to determine the optimal supplier are summarized as follows:
Step1. The fuzzy set theory was applied to determine the linguistic preferences of the
proposed model. To this end, linguistic variables were defined for several levels of preference
(Table 1). The TFNs used to represent the preferences are depicted in Fig. 2.
Table 1. Two linguistic variables for criteria and alternatives (importance and performance
level)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(Criteria)
TFNs  G
(Alternative)
TFNs  w
VL
L
M
H
(0.00, 0.00, 0.20)
(0.20, 0.30, 0.40)
(0.40, 0.50, 0.60)
(0.60, 0.70, 0.80)
VP
P
F
G
(0.00, 0.00, 0.30)
(0.20, 0.30, 0.40)
(0.35, 0.50, 0.65)
(0.60, 0.70, 0.80)
VH
(0.80, 1.00, 1.00)
VG
(0.75, 1.00, 1.00)
A fuzzy weighted sum performance matrix (P) was derived for the criteria by
multiplying the fuzzy weight vector by the decision matrix.
 a1

p   ...
 an
, b1
...
, bn
,c1 

... 
, cn 
(8)
where n represents the number of criteria.
Step 2. Defuzzification. Defuzzification was conducted according to the method of Pan
(2008); thus, TFN were used to transform the total weighted performance matrices into
interval performance matrices, providing αa and αc for each criterion:
  a1  b1

p   ... ....
  an  b n

, c1 

... 
, cn 
(9)
where n is the number of criteria.
  a    (b  a)  a

  c  c    ( c  b)
(10)
The last step of the defuzzification process was to convert interval matrices into crisp
values by applying the Lambda function, which represents the attitude of the evaluator.
Evaluators with optimistic, moderate and pessimistic attitudes take on maximum, intermediate
or minimum Lambda values on the interval [0, 1], respectively:
W 1j 


W 2 
Wj   j 
 ..... 
 k 
W j 
W j    c  (1   )  b
(11)
where W j are crisp values corresponding to Lambda, λ=0.5,
and were normalized to
comparable scales.
Step 3. TFNs were used to obtain a rating of each criterion. The value of each rating was
obtained from the following expression:
 wj 

1
 w1j  w2j  .......  wkj
K

(12)
where  wkj ( j  1,2,..........n) are the weights of the Kth expert and can be described by
k
the TFNs  wkj  [w j , w j ] .
k
 Gij 

1
 Gij1  Gij2  .......  Gijk
K

(13)
where  Gijk (i  1,2,.....m; j  1,2,..........n) are the weights of the Kth expert and can be
k
described by the TFNs  G kj  [G j , G j ] .
k
Each expert group contains K experts. The criteria weights, wj, were obtained from the
following procedure:
Step 4. Establish the grey decision matrix
  G 11

  G 21
D   ..

 ..
  G m1

 G 12
 G 22
..
..
 G m2
..
..
..
..
..
..
..
..
..
..
 G1n
 G2 n
..
..
 Gmn
where  Gij are based on TFNs.
Step 5. Establish the normalized grey decision matrix








(14)
  G*11

*
  G 21
D*   ..

 ..
  G*m1

 G*12
 G*22
..
..
 G *m 2
..
..
..
..
..
 G1*n
 G2*n
..
..
*
 Gmn
..
..
..
..
..








(15)
 G ij G ij 
For a benefit criteria,  Gij* was expressed as  Gij*   max
, max  ,
G j 
 G j
G
max
j
 
 G min

G min
j
was expressed as  G  
, j ,
 G ij G ij 
 max 1i  m G ij . For other criteria,  G
*
ij
*
ij
G min
 min 1i  m Gij  . Normalization was conducted to preserve the property that the range of
j
normalized TFNs was located on the interval [0, 1]
Step 6. By considering the importance of each criterion, the weighted normalized grey
decision matrix was established as:
 V

 V
D*   ..

 ..
 V

11
21
m1
 V 12
 V 22
..
..
 V m2
..
..
..
..
..
 V1n
 V2 n
..
..
 Vmn
..
..
..
..
..








(16)
where  Vij  Gij*  w j
Step 7. The ideal alternative was established as the reference alternative. Thus, for m possible
alternative sets, A = {A1, A2 ,…., Am}, the ideal referential alternative


Amax   G1max ,G2max ,................  Gnmax , was obtained from the following expression:
Amax 
  max V , max V ,  max V , max V , ............. max V , max V  
1im
i1
1im
i1
1im
i2
1im
i2
1im
in
1im
in
(17)
Step 8. The grey degree between compared alternatives (A = {A1, A2, …. Am}) and the ideal
alternative (Amax) was calculated, and the alternatives were ranked according to suitability. As

P Ai  Amax

 decreased, the rank of Ai increased.

P Ai  Amax 

1 n
 p Vij  G max
j
n j 1

(18)
RESULTS
To illustrate the utility of the proposed evaluation method, the model was applied to an
actual firm. In the case study, the firm continues to improve its manufacturing processes and
faces the challenges of environmental management and SCM. To deal with the requirements
of supplier selection, the firm must implement GSCM criteria from relevant environmental
regulations. To this end, the firm created an expert team consisting of four professors, two
vice presidents and four management professionals with extensive experience.
4.1 Case information
Due to the prosperity of the electronic consumer products and network market, a plant
was built in Taiwan to produce IC substrates and IC packing fields, to meet consumer
demands in 2010. Currently, the firm is the largest professional printed circuit board (PCB)
and original equipment manufacturer (OEM) in Taiwan and is the fifth ranked producer in the
world. To offer the best services, the firm is continuing to develop next generation technology,
enhance their competitiveness and satisfy customer demands. Moreover, due to the rapid
replacement rate of electronic products, the firm continues to develop green products and new
green technologies to comply with customer requirements. For the firm to sustain in a
competitive market, proper GSCM is essential.
The chief executive officer wants to understand the role of GSCM, especially in the
green market. Therefore, to develop the firm’s GSCM criteria, this assessment was presented
to the expert group. By complying with the requirement outlined in RoHS and WEEE
directives, the firm benefited from this evaluation by acquiring purchasing orders from the
USA and the European Union. In the case study, the firm’s four green suppliers were analyzed.
The expert group identified an analytical and systematic method of evaluating the
management procedures of the suppliers. To select the optimal supplier, the experts should
adopt an evaluation method from the proposed criteria. The analysis outlined in this paper
would provide recommendations to the firm and would be useful for efficient and effective
GSCM implementation.
4.2 Empirical result
In this study, the eight proposed steps were followed to analyze the data provided by the
experts. The analysis was based on four alternatives Ai = (i =1, 2, 3, 4) and 16 criteria Cj (j =
1, 2, 3,….,16), as shown in Fig. 1. According to Eq. (8), the weights of the criteria were
obtained from the group of experts and are shown in Table 2. The weights of the four
suppliers were obtained from Eq. (9), and the results are shown in Table 3.
Table 2. Criterion important weights
 wj
Cj
D1
D2
….
D 10
C1
(0.00, 0.00, 0.20)
(0.60, 0.70, 0.80)
….
(0.40, 0.50, 0.60)
0.35
0.60
C2
(0.40, 0.50, 0.60)
(0.40, 0.50, 0.60)
….
(0.60, 0.70, 0.80)
0.50
C3
(0.40, 0.50, 0.60)
(0.60, 0.70, 0.80)
….
(0.40, 0.50, 0.60)
C4
(0.60, 0.70, 0.80)
(0.60, 0.70, 0.80)
….
C5
(0.60, 0.70, 0.80)
(0.80, 1.00, 1.00)
C6
(0.60, 0.70, 0.80)
C7
Weights
Ranking
0.90
0.617
12
0.60
0.90
0.667
9
0.40
0.60
0.90
0.633
11
(0.60, 0.70, 0.80)
0.60
0.65
0.80
0.683
8
….
(0.60, 0.70, 0.80)
0.50
0.80
0.90
0.733
6
(0.00, 0.00, 0.20)
….
(0.80, 1.00, 1.00)
0.40
0.65
0.80
0.617
12
(0.80, 1.00, 1.00)
(0.80, 1.00, 1.00)
….
(0.80, 1.00, 1.00)
0.65
0.80
0.90
0.783
3
C8
(0.80, 1.00, 1.00)
(0.40, 0.50, 0.60)
….
(0.00, 0.00, 0.20)
0.50
0.60
0.70
0.600
13
C9
(0.40, 0.50, 0.60)
(0.80, 1.00, 1.00)
….
(0.60, 0.70, 0.80)
0.53
0.60
0.80
0.643
10
C10
(0.80, 1.00, 1.00)
(0.60, 0.70, 0.80)
….
(0.60, 0.70, 0.80)
0.50
0.80
0.90
0.733
6
C11
(0.40, 0.50, 0.60)
(0.80, 1.00, 1.00)
….
(0.80, 1.00, 1.00)
0.60
0.60
0.70
0.633
11
C12
(0.60, 0.70, 0.80)
(0.60, 0.70, 0.80)
….
(0.60, 0.70, 0.80)
0.70
0.75
0.85
0.767
4
C13
(0.40, 0.50, 0.60)
(0.40, 0.50, 0.60)
….
(0.40, 0.50, 0.60)
0.60
0.70
0.80
0.700
7
C14
(0.60, 0.70, 0.80)
(0.60, 0.70, 0.80)
….
(0.60, 0.70, 0.80)
0.70
0.80
0.90
0.800
2
C15
(0.60, 0.70, 0.80)
(0.40, 0.50, 0.60)
….
(0.40, 0.50, 0.60)
0.80
0.80
0.90
0.833
1
C16
(0.40, 0.50, 0.60)
(0.60, 0.70, 0.80)
….
(0.60, 0.70, 0.80)
0.70
0.70
0.85
0.750
5
Table 3. Four alternative performance weights under firm’s GSCM criteria
 G ij
Cj
Ai
D1
D2
….
D10
C1
A1
(0.20, 0.30, 0.40)
(0.35, 0.50, 0.65)
….
(0.35, 0.50, 0.65)
0.55
0.65
0. 75
A2
(0.35, 0.50, 0.65)
(0.35, 0.50, 0.65)
….
(0.20, 0.30, 0.40)
0.65
0.85
0.90
A3
(0.60, 0.70, 0.80)
(0.20, 0.30, 0.40)
….
(0.60, 0.70, 0.80)
0.45
0.60
0.75
A4
(0.75, 1.00, 1.00)
(0.35, 0.50, 0.65)
….
(0.35, 0.50, 0.65)
0.75
0.85
0.95
A1
(0.60, 0.70, 0.80)
(0.20, 0.30, 0.40)
….
(0.35, 0.50, 0.65)
0.65
0.85
0.90
A2
(0.20, 0.30, 0.40)
(0.60, 0.70, 0.80)
….
(0.20, 0.30, 0.40)
0.70
0.75
0.85
A3
(0.75, 1.00, 1.00)
(0.20, 0.30, 0.40)
….
(0.35, 0.50, 0.65)
0.65
0.85
0.95
A4
(0.75, 1.00, 1.00)
(0.20, 0.30, 0.40)
….
(0.75, 1.00, 1.00)
0.35
0.65
0.80
A1
(0.75, 1.00, 1.00)
(0.35, 0.50, 0.65)
….
(0.35, 0.50, 0.65)
0.65
0.85
0.95
A2
(0.35, 0.50, 0.65)
(0.75, 1.00, 1.00)
….
(0.35, 0.50, 0.65)
0.45
0.65
0.75
A3
(0.35, 0.50, 0.65)
(0.35, 0.50, 0.65)
….
(0.35, 0.50, 0.65)
0.65
0.85
0.95
A4
(0.75, 1.00, 1.00)
(0.35, 0.50, 0.65)
….
(0.35, 0.50, 0.65)
0.45
0.85
0.95
C2
C3
C4
C5
C16
A1
(0.75, 1.00, 1.00)
(0.20, 0.30, 0.40)
….
(0.60, 0.70, 0.80)
0.40
0.60
0.75
A2
(0.20, 0.30, 0.40)
(0.35, 0.50, 0.65)
….
(0.60, 0.70, 0.80)
0.45
0.65
0.75
A3
(0.75, 1.00, 1.00)
(0.35, 0.50, 0.65)
….
(0.20, 0.30, 0.40)
0.50
0.65
0.70
A4
(0.20, 0.30, 0.40)
(0.75, 1.00, 1.00)
….
(0.60, 0.70, 0.80)
0.35
0.55
0.65
A1
(0.75, 1.00, 1.00)
(0.20, 0.30, 0.40)
….
(0.60, 0.70, 0.80)
0.65
0.85
0.95
A2
(0.60, 0.70, 0.80)
(0.60, 0.70, 0.80)
….
(0.20, 0.30, 0.40)
0.45
0.75
0.75
A3
(0.20, 0.30, 0.40)
(0.75, 1.00, 1.00)
….
(0.75, 1.00, 1.00)
0.65
0.85
0.85
A4
(0.60, 0.70, 0.80)
(0.35, 0.50, 0.65)
….
(0.35, 0.50, 0.65)
0.45
0.75
0.85
…
…
…
…
…
…
…
….
…
…
…
…
…
…
…
….
…
…
…
…
…
…
…
….
…
…
…
…
…
…
…
….
A1
(0.75, 1.00, 1.00)
(0.60, 0.70, 0.80)
….
(0.20, 0.30, 0.40)
0.55
0.85
0.95
A2
(0.60, 0.70, 0.80)
(0.20, 0.30, 0.40)
….
(0.35, 0.50, 0.65)
0.50
0.70
0.85
A3
(0.35, 0.50, 0.65)
(0.35, 0.50, 0.65)
….
(0.60, 0.70, 0.80)
0.55
0.65
0.85
A4
(0.20, 0.30, 0.40)
(0.35, 0.50, 0.65)
….
(0.60, 0.70, 0.80)
0.45
0.65
0.75
Step1. In step 1, the expert’s opinions on linguistic preferences of performance measures
were collected and transformed according to the TFN membership functions provided in
Table 1. The six definitions used to apply the following computational steps are denoted in
Eqs. (1) - (6)
Step 2. 16 criteria and four alternatives were measured in the TFN. The defuzzification
process employed Eqs. (9) - (10). The TFN was applied to transform the total weighted
performance matrices into interval performance matrices, providing αa and αc .Using Eq. (11),
W j was transformed into crisp values corresponding to Lambda values on comparable scales.
Step 3. Using Eq. (12) and (13), TFNs for the ratings were calculated to obtain the criteria
rating value, and the results are presented in Table 2 (  w j) and 3 (  G ij).  w j was
defuzzified into the weights and ratings of each criteria.
Step 4. In step 4, the grey decision matrix of alternatives was established according to Eq.
(14).
Step 5. The grey decision matrix was normalized according to Eq. (15), and the resulting grey
normalized decision table is shown in Table 4.
Step 6. According to Eq. (16), the weighted normalized grey decision matrix was obtained,
and the results are shown in Table 5.
Step 7. The ideal alternative, Amax (the reference alternative), was calculated according to Eq.
(17), and values of [0.614, 1.000], [0.574, 0.971], [0.547, 0.936], [0.486, 0.864] were
obtained.
Table 4. Grey normalized decision matrix
C1
C2
C3
C4
C5
C6
C7
C8
C9
A1
0.735
0.898
0.825
1.000
0.818
0.780
0.962
0.825
0.825
1.000
1.000
1.000
0.825
1.000
0.825
1.000
0.780
0.962
A2
0.769
0.932
0.788
0.964
0.818
0.742
0.924
0.715
0.715
0.891
0.891
1.000
0.752
0.927
0.715
0.891
0.742
0.924
A3
0.735
0.898
0.825
1.000
0.742
0.780
0.962
0.825
0.825
1.000
1.000
0.924
0.825
1.000
0.788
0.964
0.780
0.962
A4
0.837
1.000
0.752
0.927
0.780
0.818
1.000
0.752
0.752
0.927
0.927
0.962
0.752
0.927
0.752
0.927
0.818
1.000
C10
C11
C12
C13
C14
C15
C16
A1
0.735
0.898
0.825
1.000
0.625
0.818
0.962
0.825
0.825
1.000
1.000
0.737
0.825
1.000
A2
0.769
0.932
0.788
0.964
0.818
0.742
0.924
0.715
0.715
0.891
0.891
1.000
0.752
0.927
A3
0.735
0.898
0.825
1.000
0.742
0.780
0.962
0.752
0.825
1.000
1.000
0.924
0.805
1.000
A4
0.837
1.000
0.752
0.927
0.780
0.818
1.000
0.745
0.752
0.925
0.826
0.962
0.752
0.927
Table 5. Grey weighted normalized decision matrix
C1
C2
C3
C4
C5
C6
C7
C8
C9
A1
0.593
0.879
0.636
0.943
0.607
0.907
0.544
0.836
0.636
0.943
0.607
0.907
0.546
0.838
0.657
0.965
0.755
0.962
A2
0.620
0.912
0.552
0.840
0.580
0.874
0.544
0.836
0.580
0.874
0.526
0.808
0.520
0.805
0.655
0.831
0.654
0.924
A3
0.593
0.879
0.636
0.943
0.607
0.907
0.493
0.772
0.636
0.943
0.580
0.874
0.546
0.838
0.745
0.855
0.585
0.962
A4
0.675
0.979
0.580
0.874
0.553
0.841
0.518
0.804
0.580
0.874
0.553
0.841
0.573
0.871
0.652
0.755
0.836
0.952
C10
C11
C12
C13
C14
C15
C16
A1
0.735
0.898
0.825
0.950
0.685
0.818
0.655
0.825
0.825
0.921
0.758
0.855
0.796
0.862
A2
0.769
0.932
0.788
0.964
0.755
0.835
0.458
0.685
0.715
0.891
0.831
0.956
0.752
0.927
A3
0.735
0.898
0.825
0.965
0.589
0.742
0.752
0.825
0.825
0.911
0.756
0.924
0.825
0.965
A4
0.837
0.925
0.752
0.927
0.652
0.780
0.555
0.752
0.752
0.927
0.852
0.962
0.752
0.927
Step 8. The grey degree of the four alternatives, (A1, A2, A3, A4), was calculated from Eq.
(18), and a ranking of the alternatives was obtained. The grey degrees of the alternatives were
P( A1  Amax )  0.522, P( A2  Amax )  0.555, P( A3  Amax )  0.541, P( A4  Amax )  0.552. The
smallest value indicates the best alternative; thus, A1 is the optimal supplier. Moreover, the
following trend in suppliers was observed: A1>A3>A4>A2. Hence, to achieve the firm’s
GSCM criteria, supplier A1 is an important alternative.
MAMAGERIAL IMPLICATIONS
The framework can be used to evaluate the impact of various supplier selection activities
and can provide a mechanism of monitoring and establishing evaluation platforms for firms in
the green supply chain. In previous studies, the firm’s GSCM procedures were highly variable;
however, a clear link to the firm’s decision was not observed. Indeed, the analyses presented
in previous studies were based on only a few variables, and single variable models were not
sufficient at explaining GSCM criteria. These results indicate that GSCM is a multi-criteria
concept based on upstream or downstream selection in the supply chain. When evaluating the
impact of a firm’s GSCM activities, the overall enhancement in production and its effect on
the organization must be considered.
By examining the 16 criteria, the proposed framework allows managers and researchers
to better understand the differences in operations, activities and specific management
interventions. The framework allows the firm to control and evaluate management practices
and can describe the firm’s supplier selection dilemmas. For example, in step 8, a value is
placed on the overall importance of the evaluator’s perception to the four alternatives. Here,
the top five criteria and corresponding values were: 1. to reduce the use of hazardous products
in the production process (C15- 0.833); 2. support of management (C14- 0.800); 3. quality of
service (C7- 0.783); 4. the applicability of internal green production plans (C12- 0.767); 5. the
presence of environmental management systems (C16- 0.750). The GSCM criteria were
analyzed by the experts, and the performance of the supplier was determined primarily by the
reduction of hazardous products in the production process and management support.
The results of the case study are similar to those of Yao et al. (2007), who found that
management support and external influences are important determinants. Moreover, perceived
benefits to customers or suppliers, and internal benefits affect the use of
electronically-enabled supply chains. Tseng et al. (2009a) studied sustainable production
indicators, and found that two major criteria contributed to sustainable production, including a
reduction in waste generated by contracted service/material providers and a reduction in the
amount of hazardous waste generated by the supplier. In a broader sense, the framework can
be used as an analytical tool to develop and construct a strategic environmental development
plan and GSCM criteria for the firm. To achieve optimal results, managers should understand
the firm’s GSCM evaluation criteria, including the presence of linguistic preferences and
incomplete information.
This study proved that the manager must be aware that the firm’s GSCM is not just a
black box. Through the proposed framework, managers are able to capture a fairly complete
picture of the firm’s GSCM. In other words, managers may find that the proposed framework
for the assessment of GSCM criteria is a useful method for reviewing and improving strategic
development plans and performance evaluations, which may lead to enhanced productivity
and competitive advantage.
For firms that intend to evaluate suppliers with the proposed criteria, this study offers
several benefits. The main contribution of this study is the hierarchical model presented in Fig.
1. This model provides a structured and logical method of synthesizing judgments that can be
used for the evaluation of appropriate suppliers. The model is a useful guideline that helps
structure a difficult and often emotional decision. The second benefit of this study is the
development of criteria based on a comprehensive review. Moreover, the features of a firm’s
GSCM have been examined and identified.
The model developed in this study provides an overview of a firm’s decision-making
process in the presence of incomplete information. Moreover, firms can better understand the
evaluation criteria of GSCM by applying the proposed model. The methodology outlined in
this study is particularly useful for making decisions based on multiple criteria in the presence
of linguistic preferences and incomplete information. Moreover, the framework can be
customized and used for the selection of suppliers and management activities. To apply the
proposed methodology, the evaluator must remove irrelevant criteria and include criteria that
are applicable to their firm. Thus, a firm’s GSCM can be based on many different types of
criteria and can be modified and refined as necessary.
Furthermore, this study proposed a hybrid MCDM for selecting alternatives in the
presence of uncertainty. However, the evaluator’s judgment is often uncertain, and incomplete
information cannot always be evaluated with exact numbers. An empirical example of green
supplier selection was used to illustrate the application of the proposed criteria in an OEM
firm. The experimental results indicated that the proposed approach is reliable and reasonable,
and an optimal alternative was selected from the four possible choices. The proposed model
can easily and effectively accommodate validated criteria. The proposed model establishes a
foundation for future research and is appropriate for predicting uncertain criteria. To improve
the firm’s performance and provide information that will have the greatest effect on reducing
uncertainty, a firm can apply this model to evaluate and determine the optimal GSCM
supplier.
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